WIAS Preprint No. 2310, (2016)

Corrector estimates for a thermo-diffusion model with weak thermal coupling



Authors

  • Muntean, Adrian
  • Reichelt, Sina

2010 Mathematics Subject Classification

  • 35B27 35Q79 74A15 78A48

Keywords

  • Homogenization, corrector estimates, periodic unfolding, gradient folding operator, perforated domain, thermo-diffusion, composite media

Abstract

The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology ``weak thermal coupling'' refers here to the variable scaling in terms of the small homogenization parameter ε of the heat conduction-diffusion interaction terms, while the ``high-contrast'' is thought particularly in terms of the heat conduction properties of the composite material. As main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with ε-independent estimates for the thermal and concentration fields and for their coupled fluxes

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